Financial terms of the deal were not announced.
The 26-year-old Bryzgalov had a 13-12-1 record and a 2.51 GAA in 31 regular-season games. He had a 1.46 GAA, a .944 save percentage and three shutouts in the postseason, when he became the first rookie to post consecutive shutouts since 1945.
Bryzgalov, who beat out Jean-Sebastian Giguere, helped the Ducks beat Colorado and Calgary in the playoffs before they lost to Edmonton in five games in the Western Conference finals.
Bryzgalov was the 44th overall pick in the 2000 NHL draft. Before last season, he had played in two NHL games -- one in the 2001-02 season and another in the 2003-04 season.